Great summary.
I'm using a combination of FreshRSS (self-hosted) and Readrops (for Android).
I feel like #1 is handled by this combination. But, I wonder what convergent means here for you?
I don't notice any performance issues. But, this feels like a simple task for a bunch of RSS feeds. Did you notice performance issues with other readers?
There is something very interesting about what you call "automagical discovery." To me this is the biggest hole in my RSS experience. I want something that gives me magical discovery within the feeds I have based on my reading experiences. I subscribe to a lot of feeds because of one article, and then don't care about 90% of the other articles, but there are 10% that I do really want to read, but don't have the focus to find them. Is that what you mean by automagical?
Why do you want #4?
Filtering by keywords seems interesting.
FreshRSS has a bunch of analytics that comes with the server. I never really use it, but it is interesting. I would be happy to share what I can see based on my limited usage over a few months if this would serve your purposes. I would be interested in understanding what you mean by that.
The one thing I wish I had in my current setup is a way to take notes in a centralized way. When I'm on Android, I suppose I can copy and use a share intent. And, on a browser, I could install an extension to do that. But, it feels like that is an interesting opportunity for someone. I wish FreshRSS could layer a JavaScript app on posts, for example, and then I could build whatever I want. It has an extension API, but strangely documented.
Thanks!